Question

From a sample of 37 graduate​ students, the mean number of months of work experience prior to entering an MBA program was 35.15. The national standard deviation is known to be 18 months. What is a 95​% confidence interval for the population​ mean?

Answer 1

Answer: (29.35, 40.95)

Step-by-step explanation:

Formula to find the confidence interval for population mean :-

$\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}$

, where $\overline{x}$ = sample mean.

z*= critical z-value

n= sample size.

$\sigma$ = Population standard deviation.

As per given , we have

$\overline{x}=35.15$

$\sigma=18$

n= 37

Using z-table, the critical z-value for 95% confidence = z* = 1.96

Then, the confidence interval for the population mean will be :

$35.15\pm (1.96)\dfrac{18}{\sqrt{37}}$

$=35.15\pm (1.96)\dfrac{1.7}{6.08276}$

$=35.15\pm (1.96)(2.95918)$

$\approx35.15\pm5.80$

$=(35.15-5.80,\ 35.15+5.80)=(29.35,\ 40.95)$

Hence, a 95​% confidence interval for the population​ mean = (29.35, 40.95)